Euclidean and Non-euclidean Geometries
Euclidean and Non-euclidean Geometries

Author: Maria Helena Noronha

Publisher:

Published: 2002

Total Pages: 440

ISBN-13:

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This book develops a self-contained treatment of classical Euclidean geometry through both axiomatic and analytic methods. Concise and well organized, it prompts readers to prove a theorem yet provides them with a framework for doing so. Chapter topics cover neutral geometry, Euclidean plane geometry, geometric transformations, Euclidean 3-space, Euclidean n-space; perimeter, area and volume; spherical geometry; hyperbolic geometry; models for plane geometries; and the hyperbolic metric.

A History of Non-Euclidean Geometry
A History of Non-Euclidean Geometry

Author: Boris A. Rosenfeld

Publisher: Springer Science & Business Media

Published: 2012-09-08

Total Pages: 481

ISBN-13: 1441986804

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The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.

Euclidean and Non-Euclidean Geometries
Euclidean and Non-Euclidean Geometries

Author: Marvin J. Greenberg

Publisher: Macmillan

Published: 1993-07-15

Total Pages: 512

ISBN-13: 9780716724469

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This classic text provides overview of both classic and hyperbolic geometries, placing the work of key mathematicians/ philosophers in historical context. Coverage includes geometric transformations, models of the hyperbolic planes, and pseudospheres.

Modern Geometries
Modern Geometries

Author: Michael Henle

Publisher: Pearson

Published: 2001

Total Pages: 404

ISBN-13:

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Engaging, accessible, and extensively illustrated, this brief, but solid introduction to modern geometry describes geometry as it is understood and used by contemporary mathematicians and theoretical scientists. Basically non-Euclidean in approach, it relates geometry to familiar ideas from analytic geometry, staying firmly in the Cartesian plane. It uses the principle geometric concept of congruence or geometric transformation--introducing and using the Erlanger Program explicitly throughout. It features significant modern applications of geometry--e.g., the geometry of relativity, symmetry, art and crystallography, finite geometry and computation. Covers a full range of topics from plane geometry, projective geometry, solid geometry, discrete geometry, and axiom systems. For anyone interested in an introduction to geometry used by contemporary mathematicians and theoretical scientists.

Introduction to Non-Euclidean Geometry
Introduction to Non-Euclidean Geometry

Author: Harold E. Wolfe

Publisher: Courier Corporation

Published: 2012-01-01

Total Pages: 274

ISBN-13: 0486498506

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One of the first college-level texts for elementary courses in non-Euclidean geometry, this volumeis geared toward students familiar with calculus. Topics include the fifth postulate, hyperbolicplane geometry and trigonometry, and elliptic plane geometry and trigonometry. Extensiveappendixes offer background information on Euclidean geometry, and numerous exercisesappear throughout the text.Reprint of the Holt, Rinehart & Winston, Inc., New York, 1945 edition

Taxicab Geometry
Taxicab Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

Published: 2012-04-30

Total Pages: 99

ISBN-13: 048613606X

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Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.

A Simple Non-Euclidean Geometry and Its Physical Basis
A Simple Non-Euclidean Geometry and Its Physical Basis

Author: I.M. Yaglom

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 326

ISBN-13: 146126135X

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There are many technical and popular accounts, both in Russian and in other languages, of the non-Euclidean geometry of Lobachevsky and Bolyai, a few of which are listed in the Bibliography. This geometry, also called hyperbolic geometry, is part of the required subject matter of many mathematics departments in universities and teachers' colleges-a reflec tion of the view that familiarity with the elements of hyperbolic geometry is a useful part of the background of future high school teachers. Much attention is paid to hyperbolic geometry by school mathematics clubs. Some mathematicians and educators concerned with reform of the high school curriculum believe that the required part of the curriculum should include elements of hyperbolic geometry, and that the optional part of the curriculum should include a topic related to hyperbolic geometry. I The broad interest in hyperbolic geometry is not surprising. This interest has little to do with mathematical and scientific applications of hyperbolic geometry, since the applications (for instance, in the theory of automorphic functions) are rather specialized, and are likely to be encountered by very few of the many students who conscientiously study (and then present to examiners) the definition of parallels in hyperbolic geometry and the special features of configurations of lines in the hyperbolic plane. The principal reason for the interest in hyperbolic geometry is the important fact of "non-uniqueness" of geometry; of the existence of many geometric systems.

Experiencing Geometry
Experiencing Geometry

Author: David Wilson Henderson

Publisher: Prentice Hall

Published: 2005

Total Pages: 438

ISBN-13:

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The distinctive approach of Henderson and Taimina's volume stimulates readers to develop a broader, deeper, understanding of mathematics through active experience--including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe. The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles, projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra. For mathematics educators and other who need to understand the meaning of geometry.